Index and Stability in Bimatrix Games :
Schemde, Arndt.
Index and Stability in Bimatrix Games : A Geometric-Combinatorial Approach / by Arndt Schemde. - x, 151 páginas recurso en línea. - Lecture Notes in Economics and Mathematical Systems, 560 0075-8442 ; .
Springer eBooks
Eqilibrium Components with Arbitrary Index -- A Reformulation of the Index for Equilibria in Bimatrix Games -- Sperner’s Lemma and Labelling Theorems -- A Strategic Characterisation of the Index -- Outside Option Equilibrium Components -- Index Zero and Hyperstability.
The index of an equilibrium in a game gives information about the "stability" of the equilibrium, for example with respect to game dynamics. Unfortunately, index theory is often very technical. This book presents a new geometric construction that visualises the index in an intuitive way. For example, a 3×n game, for any n, can be represented by a figure in the plane, from which one can read off any equilibrium, and its index as a geometric orientation. With this insight, the index can be characterised in strategic terms alone. Moreover, certain "hyperstable" equilibrium components are seen to have nonzero index. The construction gives an elementary proof that two-player games have a Nash equilibrium, and, in an unusual direction, the powerful fixed point theorem of Brouwer.
9783540291022
10.1007/3540291024 doi
HB144
Index and Stability in Bimatrix Games : A Geometric-Combinatorial Approach / by Arndt Schemde. - x, 151 páginas recurso en línea. - Lecture Notes in Economics and Mathematical Systems, 560 0075-8442 ; .
Springer eBooks
Eqilibrium Components with Arbitrary Index -- A Reformulation of the Index for Equilibria in Bimatrix Games -- Sperner’s Lemma and Labelling Theorems -- A Strategic Characterisation of the Index -- Outside Option Equilibrium Components -- Index Zero and Hyperstability.
The index of an equilibrium in a game gives information about the "stability" of the equilibrium, for example with respect to game dynamics. Unfortunately, index theory is often very technical. This book presents a new geometric construction that visualises the index in an intuitive way. For example, a 3×n game, for any n, can be represented by a figure in the plane, from which one can read off any equilibrium, and its index as a geometric orientation. With this insight, the index can be characterised in strategic terms alone. Moreover, certain "hyperstable" equilibrium components are seen to have nonzero index. The construction gives an elementary proof that two-player games have a Nash equilibrium, and, in an unusual direction, the powerful fixed point theorem of Brouwer.
9783540291022
10.1007/3540291024 doi
HB144